To find the total surface area of the cuboid, we need to first determine its dimensions based on the given volume.
Let the dimensions of the cuboid be represented as 5x, 2x, and x, where x is a common multiplier. The volume of a cuboid is calculated as:
Volume = Length × Breadth × Height
Substituting the dimensions into the volume formula gives us:
1250 = 5x × 2x × x
This simplifies to:
1250 = 10x³
Now, to solve for x³, we divide both sides by 10:
x³ = 125
Taking the cube root of both sides, we find:
x = 5
Now substituting x back into our expressions for the dimensions, we get:
- Length = 5x = 5 * 5 = 25 meters
- Breadth = 2x = 2 * 5 = 10 meters
- Height = x = 5 meters
Next, we can calculate the total surface area of the cuboid using the formula:
Surface Area = 2(Length × Breadth + Breadth × Height + Height × Length)
Substituting in the values we found:
Surface Area = 2(25 × 10 + 10 × 5 + 5 × 25)
This simplifies to:
Surface Area = 2(250 + 50 + 125)
Surface Area = 2(425) = 850 square meters
Thus, the total surface area of the cuboid is 850 square meters.